34 citations · 140 across the 46 of their papers we have counts for
10 papers · 1 filter
The Torelli locus and Newton polygons
Rachel Pries
This manuscript is about abelian varieties that are Jacobians of curves. I started writing it for a lecture series at the Arizona Winter School in 2024 on abelian varieties. A long…
Mass formula for non-ordinary curves in one dimensional families
Renzo Cavalieri, Rachel Pries
This paper is about one dimensional families of cyclic covers of the projective line in positive characteristic. For each such family, we study the mass formula for the number of n…
Abhyankar's conjectures in Galois theory: Current status and future directions
David Harbater, Andrew Obus, Rachel Pries +1
In this paper, we survey the major contributions of Abhyankar to the development of the theory of fundamental groups and Galois covers in positive characteristic. We first discuss…
Ekedahl-Oort strata of hyperelliptic curves in characteristic 2
Arsen Elkin, Rachel Pries
Suppose is a hyperelliptic curve of genus defined over an algebraically closed field of characteristic . We prove that the de Rham cohomology of decomposes int…
A survey of Galois theory of curves in characteristic p
Rachel Pries, Katherine Stevenson
This survey is about Galois theory of curves in characteristic p, a topic which has inspired major research in algebraic geometry and number theory and which contains many open que…
The p-rank strata of the moduli space of hyperelliptic curves
Jeff Achter, Rachel Pries
We prove results about the intersection of the p-rank strata and the boundary of the moduli space of hyperelliptic curves in characteristic p > 2. Using this, we prove that the Z/\…